The distance of the point $(2, 3, 4)$ from the plane $3x - 6y + 2z + 11 = 0$ is

If the equation of the plane passing through the point $(1, 1, 2)$ and perpendicular to the intersection of the planes $x - 3y + 2z - 1 = 0$ and $4x - y + z = 0$ is $Ax + By + Cz = 1$,then $140(C - B + A)$ is equal to $.........$.

The line of intersection of the planes $\overline{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$ and $\overline{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2$ is parallel to which of the following vectors?

The equation of the plane passing through the points $(3, 2, 2)$ and $(1, 0, -1)$ and parallel to the line $\frac{x - 1}{2} = \frac{y - 1}{-2} = \frac{z - 2}{3}$ is:

If $\lambda_1 < \lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r} \cdot (3 \hat{i} - 5 \hat{j} + \hat{k}) = 7$ and $P_2: \vec{r} \cdot (\lambda \hat{i} + \hat{j} - 3 \hat{k}) = 9$ is $\sin^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$,then the square of the length of the perpendicular from the point $(38 \lambda_1, 10 \lambda_2, 2)$ to the plane $P_1$ is $...........$.

The plane through the intersection of planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $Y$-axis also passes through the point